How do you write an exponential equation that passes through (-1, .5) and (2, 10)?

Aug 5, 2015

I found: color(red)(y=0.5e^(1+x)

Explanation:

In general the equation will be of the form:
$y = k {e}^{c x}$
where: $k \mathmr{and} c$ are constants to be found:
let us use our points and substitute into our general equation:
$\left\{\begin{matrix}0.5 = k {e}^{- c} \\ 10 = k {e}^{2 c}\end{matrix}\right.$
from the first:
$k = \frac{0.5}{e} ^ - c = 0.5 {e}^{c}$
substitute into the second:
$10 = 0.5 {e}^{c} \cdot {e}^{2 c}$
use the law of exponents and get:
${e}^{c + 2 c} = \frac{10}{0.5} = 20$
take the $\ln$ on both sides:
$3 c = \ln \left(20\right)$
$c \approx 1$
substitute back into $k = \frac{0.5}{e} ^ - c = 0.5 {e}^{c}$:
$k = 0.5 e$
so finally your equation will be:
color(red)(y=0.5e*e^x=0.5e^(1+x)

Graphically: